Amyloid formation has been implicated in the pathology of over 20 human diseases, but the rational design of amyloid inhibitors is hampered by a lack of structural information about amyloid-inhibitor complexes. We use isotope labelling and two-dimensional infrared spectroscopy to obtain a residue-specific structure for the complex of human amylin (the peptide responsible for islet amyloid formation in type 2 diabetes) with a known inhibitor (rat amylin). Based on its sequence, rat amylin should block formation of the C-terminal β-sheet, but at 8 h after mixing, rat amylin blocks the N-terminal β-sheet instead. At 24 h after mixing, rat amylin blocks neither β-sheet and forms its own β-sheet, most probably on the outside of the human fibrils. This is striking, because rat amylin is natively disordered and not previously known to form amyloid β-sheets. The results show that even seemingly intuitive inhibitors may function by unforeseen and complex structural processes.